NAME:______DATE:______CORE:______
MATH I – Unit 6 Retest Study Guide
Find the vertex, axis of symmetry, determine whether the graph has a min/max, draw the graph for the equation, and find the x-intercept and y-intercept.
1. y = 2x2 + x – 4
Axis of Symmetry:______Vertex: ______Max/Min: ______
Y-Intercept:______X-intercept: ______
2. y = -x2 – x + 2
Axis of Symmetry:______Vertex: ______Max/Min: ______Y-Intercept: ______
X-Intercept(s):______
Solve the following using your calculator.
3. You and a friend are hiking in the mountains. You want to climb to a ledge that is 20 ft above you. The height the grappling hook can be thrown is given by the function h = -16t2 – 32t + 5.
a. What is the maximum height the grappling hook can reach?
b. Can you throw it high enough to reach the ledge?
4. A flare is launched up with an initial velocity of 64 feet per second from the top of a 200 foot building. The equation h(t) = -16t2 + 64t + 200 models this situation. Determine the maximum height of the flare and time it takes to reach that maximum.
5. From 4 feet above a swimming pool, Susan throws a ball upward with a velocity of 32 feet per second. The height of the ball t seconds after Susan throws it is given by h(t) = -16t2 + 32t + 4.
a. Find the maximum height reached by the ball and the time this height is reached. (Label which one is height and which one is time.)
b. When was the ball at the same height as when it was thrown (4 feet)?
6. A rectangular piece of ground is to be enclosed on three sides by 160 ft of fencing. The fourth side is the barn. Find the dimensions of the enclosure and the maximum area that can be enclosed.
Solve by factoring.
7. 3x2 – 10x = 88. 2x2 + 7x + 10 = 0
9. x2 – 16 = 010. 7x2 – 45x – 28 = 0